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get_products_of_all_ints_except_at_index.js

function get_products_of_all_ints_except_at_index(arr) {

    var numbersBeforeIndex = [];
    var numbersAfterIndex = [];

    for (var i = 0; i < arr.length; i++) {

        numbersBeforeIndex[i] = arr.slice(0, i);
        if (numbersBeforeIndex[i].length) {
            numbersBeforeIndex[i] = numbersBeforeIndex[i].reduce(function (a, b) {
                return a * b;
            });
        }
        else {
            numbersBeforeIndex[i] = 1;
        }

        numbersAfterIndex[i] = arr.slice(i + 1, arr.length);
        if (numbersAfterIndex[i].length) {
            numbersAfterIndex[i] = numbersAfterIndex[i].reduce(function (a, b) {
                return a * b;
            });
        }
        else {
            numbersAfterIndex[i] = 1;
        }
    }

    var products = [];
    for (i = 0; i < arr.length; i++) {
        products[i] = numbersBeforeIndex[i] * numbersAfterIndex[i];
    }

    return products;
}

Work in progress.